<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ca</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>and other topological semimetals with line nodes and drumhead surface states
Bibliographic record
Abstract
Topological nodal line semimetals exhibit protected one-dimensional Fermi lines, which arise due to an intricate interplay between the symmetry and topology of the electronic wave functions. In this paper, the authors derive the $\mathbb{Z}$ invariants that guarantee the stability of the line nodes in the bulk under reflection symmetry and show that a quantized Berry phase (i.e, a ${\mathbb{Z}}_{2}$ invariant) leads to the appearance of protected surfaces states, which take the shape of a drumhead. Most importantly, a relation between the $\mathbb{Z}$ invariant, which characterizes the bulk, and the quantized Berry phase is derived. This relation is generally applicable to any topological nodal line semimetal with or without spin-orbit coupling. Moreover, it is shown that the Berry phase invariant can be simply obtained by computing the reflection parity eigenvalues. As a representative example of a topological nodal line semimetal, the authors examine Ca${}_{3}$P${}_{2}$, which has been identified as an ideal system with the line nodes at the Fermi energy. Using numerical calculations, they show that the drumhead surface state of Ca${}_{3}$P${}_{2}$ has a rather weak dispersion, which implies that correlation effects are enhanced at the surface.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.407 | 0.236 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".